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Title: Parallel strategies for estimating the vector generalized linear model Authors:  Ana Colubi - Justus Liebig University Giessen (Germany)
Erricos John Kontoghiorghes - Cyprus University of Technology and Birkbeck University of London, UK (Cyprus)
Panagiotis Paoullis - Frederick University (Cyprus) [presenting]
Abstract: Strategies for computing the estimators of Vector Generalized Linear Models (VGLMs) are investigated. VGLMs is a class of regression models that are limited only by the assumption that the regression coefficients enter through a set of linear predictors. Examples of models with this structure are related with univariate and multivariate distributions, time series, categorical data analysis, survival analysis, generalized estimating equations, correlated binary data and nonlinear least squares problems to name but a few. The algorithm employed to find the Maximum Likelihood Estimate (MLE) of the VGLM is based on the iteratively reweighted least squares (IRLS) and the Fisher scoring method. Three new methods for computing the IRLS of the VGLM are presented. The first method transforms the VGLM in each iteration to an ordinary linear model and uses the QR decomposition to find the estimate. The other two employ the generalized QR decomposition to compute the MLE of the VGLM which are formulated as iterative generalized linear least-squares problems. Various algorithms for computing the MLE of the VGLM are proposed. The algorithms are based on orthogonal transformations and exploit efficiently the Kronecker structure of the model matrix and the sparse structure of the working weight matrix. Parallel strategies for the numerical estimation of the VGLM are discussed.